Drive means such as stepper motors are conventionally employed in equipment such as X-Y plotters, printing apparatus, and the like. Such apparatus require generally incremental displacements of one or more masses. The mass (or masses) being driven in such applications are accelerated from zero velocity to a selected velocity, and then decelerated to zero velocity to complete a cycle. The masses are typically required to complete such cycles of movement in rapid succession.
Print substrates are supported by a substrate support during many types of printing operations. The substrate support may take the form of a generally planar or curved rigid surface, or a hollow, cylindrical print drum. The print substrate and a printing mechanism are typically moved relative to one another as printing material is applied to the print substrate. The print substrate may be indexed at predetermined intervals to expose different areas of the print substrate for printing.
Imprecise indexing of the print substrate may result in overshoot, ringing and noise. Overshoot occurs when the print substrate and substrate support are moved beyond the desired final position and must then be returned to the desired final position. Vibrational ringing occurs when the substrate support does not stop positively. These problems are exacerbated by frictional forces, which cause the masses to stop in unpredictable locations.
Overshoot and ringing generally result in diminished print quality, particularly in thermal phase change ink jet printers in which precise ink drop placement is critical. Throughput rates are also affected, because printing operations cannot commence until overshoot has been corrected and ringing has subsided. Additionally, imprecise indexing may result in serious acoustic noise which is objectionable from an operational standpoint.
In printer applications, the desired substrate support (e.g., print drum) motion profile is normally conveyed directly to a stepper motor, and the stepper motor generates rotational output corresponding to the desired position profile. A print drum is typically driven by a cable and pulley system or a cogged timing belt which translates the rotational motor drive output to substrate support indexing.
In general, acceleration/deceleration motion profiles may be either linear or nonlinear. An exemplary linear profile is illustrated in FIG. 1a. Linear velocity profiles are generally characterized by constant acceleration from zero or another predetermined velocity, followed by a zero acceleration constant velocity period, followed by constant deceleration to the initial velocity level. Linear profiles generally result in ringing at the inflection points of the motion profile, as shown.
Nonlinear acceleration/deceleration profiles are illustrated in FIGS. 1b and 1c. Non-linear velocity profiles of the type shown in FIG. 1b are optimized for a maximum velocity, shown as V.sub.MAX. Velocity profiles for velocities (V) lower than the maximum are simply truncated versions of the maximum velocity profile. The truncated velocity profiles may produce ringing at inflection points, as shown.
Alternatively, a plurality of nonlinear velocity profiles similar to the velocity profile for V.sub.MAX illustrated in FIG. 1b may be derived for several selected velocities and stored. This system requires substantial memory capability, however, and it may not be suitable for applications requiring a large number of programmed velocity profiles.
U.S. Pat. No. 4,648,026 teaches a microprocessor stepper motor drive which utilizes a single acceleration/deceleration motion profile regardless of the final velocity and/or position of the device being driven. The acceleration/deceleration motion profile is stored in a storage device and added to the desired final velocity to produce smooth velocity profiles corresponding to selected desired velocities, as shown in FIG. 1c.
Although the non-linear velocity profiles of the types shown in FIG. 1c are satisfactory for some systems, overshoot, ringing and acoustic noise remain problematic for high precision, rapidly cycling systems such as rotational indexing of a print drum and associated print substrate during operation of ink jet printers. Such applications require quiet, rapid and accurate movement to provide high quality printed products. The methods and apparatus of the present invention are thus directed to the derivation and implementation of motion profiles that provide quiet, rapid and precise rotational indexing of one or more masses driven, for example, by a stepper motor.